This free online hexadecimal to decimal calculator will convert hexadecimal numbers into decimal numbers and display a conversion chart to show how it arrived at the answer.
If you're not sure what a hexadecimal number is, or you would like to convert a decimal number into a hexadecimal number, please visit the Decimal to Hex Conversion page.
Hexadecimals are numbers that use the base 16 system of counting and expressing value. Instead of using just the numeric characters 09 like we're accustomed to, hexadecimals also use the letters AF to represent the values 1015. This allows us to more succinctly express or communicate numeric values than other number systems that have fewer numeric characters to work with (decimal, octal, binary).
To illustrate, suppose you were a computer programmer and you needed to write or communicate a binary number like 110110110110_{2} (the numbering system recognized by computers). The decimal equivalent of that binary number would be "3510" whereas the hexadecimal equivalent would simply be "DB6". So as you can see, the primary reason we use hexadecimals instead of other number systems is simply because they are more compact and therefore more convenient to write and communicate.
If the hexadecimal number you are converting is less than 16, then you can simply use the following hex to decimal conversion chart:
Base 16 :  0  1  2  3  4  5  6  7  8  9  A  B  C  D  E  F 
Base 10:  0  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15 
On the other hand, if the hexadecimal you are converting is greater than 15, then it helps to use a conversion method that identifies and sums place values  a method you are already familiar with for identifying place values in the decimal number system.
So, in order to help you to understand how to convert hexadecimal to decimal, it may help to recall how we translate the value of a decimal number. Lets use the decimal number 1357 (1357_{10}, or onethousand, threehundred and fiftyseven) as an example:
A  Power of 10:  10^{3}  10^{2}  10^{1}  10^{0} 
B  Place value (A result):  1000  100  10  1 
C  Entered decimal digit:  1  3  5  7 
D  Product of B * C:  1000  300  50  7 
E  Cumulative total of D:  1000  1300  1350  1357 
With the above base 10 translation in mind, here is how you would convert the base 16 number 12CA (12CA_{16} or onetwoCA) into a base 10 number:
A  Power of 16:  16^{3}  16^{2}  16^{1}  16^{0} 
B  Place value (A result):  4096  256  16  1 
C  Entered hex digit:  1  2  C  A 
D  Product of B * C:  4096  512  192  10 
E  Cumulative total of D:  4096  4608  4800  4810 
As you can see, converting a hexadecimal number to a decimal number is a simple process of identifying the hexadecimal place value of each digit, multiplying each digit by its place value, and then adding up all of the products.
With that, let's use the Hex to Decimal Converter to convert base 16 to base 10.
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Hexadecimal system: Number system that uses the base 16 system of expressing values, which consists of the digits 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E and F. Base 16 numbers are usually written with a subscripted 16 behind them (7D_{16}), a lowercase "h" behind them (7Dh), or a "0x" placed in front of them (0x7D). The hexadecimal system is often used in computer programming because it is more convenient to express values in base 16 mode than it is to express values in binary machine code.
Hexadecimal number (base 16): Enter the hexadecimal (base 16) number you would like to convert into a decimal (base 10) number. Note that the entered number may only consist of digits 09 and letters AF, a single decimal point, and the leading digit must not be a zero (also remove all hex identifiers such as 0x, h, and/or a subscripted 16).
Decimal (base 10) equivalent: This is the decimal equivalent to the entered hexadecimal number. Note that after clicking the Convert Hex to Decimal button the hex to decimal converter will display a detailed explanation of how it arrived at the result immediately below this line.
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